Thursday, January 29, 2009

Over the course of the regular season, APR picked 240 NFL games
week 2 to week 17. I am counting the Bengals @ Eagles tie
game as a push in the following tallies.

Visitor vs Home:

VisitorWon

HomeWon

Total

Picked Right

69

90

159

Picked Wrong

34

46

80

Total

103

136

239

APR picked the home team to win 124 times (90 right + 34 wrong).
Since 136 home teams won, that's pretty good evidence that some kind of
factor should be added to favor home teams in generating picks.

Picks by Matchup Ratio

The matchup ratio (ρ) for each game is the quotient of the
corresponding power indexes for each team (larger divided by the
smaller). It is intended to be an indication of "pick confidence":
ρ values near 1.0 involve teams judged to be very close in
power, while large values indicate more of a mismatch.

Range

PickedRight

#Games

%

PV+HW

PV+VW

ρ

<1.01

5

9

55.6%

2

3

1.01<=

ρ

<1.05

26

41

63.4%

9

8

1.05<=

ρ

<1.10

29

46

63.0%

11

15

1.10<=

ρ

<1.15

21

41

51.2%

9

10

1.15<=

ρ

<1.20

24

32

75.0%

5

10

1.20<=

ρ

<1.30

21

28

75.0%

5

8

1.30<=

ρ

<1.50

24

29

82.8%

3

11

1.50<=

ρ

9

13

69.2%

2

4

"PV+HW" stands for "Picked Visitor and Home Won", and indicates the
number of games in each range where APR incorrectly picked the
visitor to win (and could be picked up by giving home teams more power).

"PV+VW" stands for "Picked Visitor and Visitor Won", and
indicates the number of games in each range where APR correctly
picked the visitor to win (and could be lost by giving home teams
more power).

This indicates that simply giving home teams more power would
cost more correctly picked games (where the visiting team wins)
than it would gain.

The drop off of accuracy for ρ >= 1.50 is due to the fact
that very large values of ρ are only seen at the very
beginning of the season, when APR only has a few games to produce
power indexes.

The unweighted version of APR (i.e., all games have the same
weight) is computed for all regular season games.

The 16-game schedules are collated for each team.

For each schedule, every team on the schedule is mapped to its power index
computed in step 1. This yields a list of 16 power index values
for each team (divisional opponents are counted twice; no adjustment is made
for home vs away games).

The list of power index values is then averaged, yeilding a
"Strength of Schedule" power index for each team.

As usual, a higher power index value indicates a more difficult
schedule.

The Schedule Power Table

Ordered from weakest schedule (top) to strongest schedule (bottom).

SchedulePower

Team

Playoffs?

1.239

Buffalo Bills

1.244

San Francisco 49ers

1.249

New York Jets

1.251

Miami Dolphins

AFC #3

1.252

New England Patriots

1.262

Arizona Cardinals

NFC #4

1.267

Seattle Seahawks

1.268

Denver Broncos

1.278

Atlanta Falcons

NFC #5

1.281

San Diego Chargers

AFC #4

1.283

New Orleans Saints

1.283

Tampa Bay Buccaneers

1.283

Tennessee Titans

AFC #1

1.284

St. Louis Rams

1.290

Carolina Panthers

NFC #2

1.293

Washington Redskins

1.293

Chicago Bears

1.294

New York Giants

AFC #1

1.295

Philadelphia Eagles

NFC #6

1.296

Green Bay Packers

1.297

Oakland Raiders

1.299

Kansas City Chiefs

1.302

Dallas Cowboys

1.303

Minnesota Vikings

NFC #3

1.311

Baltimore Ravens

AFC #6

1.314

Indianapolis Colts

AFC #5

1.315

Houston Texans

1.321

Jacksonville Jaguars

1.328

Detroit Lions

1.328

Pittsburgh Steelers

AFC #2

1.344

Cincinnati Bengals

1.346

Cleveland Browns

Comments:

The range of values is actually pretty compact; relatively
small differences in schedules can make a big difference in where
a team ends up (c.f. the Titans compared to the rest of the AFC
South).

Every AFC East team is in the weakest 8, and all are weaker the
Arizona Cardinals and the San Diego Chargers.

Every NFC West team except the St. Louis Rams is also in the
weakest 8.

Every AFC North team is in the strongest 8.

Every AFC South team except the Tennessee Titans is also in the
stronget 8.

There's no obvious correlation between schedule power and
playoff appearance—the playoff teams seem to be scattered
pretty evenly; and both the #1 seeds and the NFC #2 seed are
pretty near the middle of the pack.

The Browns and Bengals placement make it hard for the Lions to
argue that they went winless because of injuries, a tough
schedule, and a bad team (though to be fair, the Browns got their
four wins before Derek Anderson and Brady Quinn were both on IR).

...but that means 16 teams were picked 9-6 (60%) or worse,
which is not so good.

8-7-0

Packers, Jets, Falcons, Redskins

The Packers (#5 to #18), Jets (#4 to #19), and Redskins (#1 to
#22) all had late season collapses, and APR did not adjust quickly
enough.

7-8-0

Buccaneers

The Bucs did not travel well. Through week 15, they were 6-0
at home, but just 3-5 on the road. And then, for good measure,
they dropped their last two home games.

6-9-0

Broncos

The Broncos win APR's "Upset King of 2008" award. They were
5-4 against teams 8-8 or better, but just 3-4 against teams with
losing records, including an inexcusable loss to the 2-14
Chiefs. How do you pick a team like that?

Comments:

APR uses a simple exponential decay rate to discount older
games. I suspect that this gives early games too much weight and
late games too little. A more S-shaped curve will probably yield
better results.

Under the current configuration, APR's worst per-team record is
for the 1987 Seahawks and 1994 Bills (both 2-13).

Kurt Warner has 770 yards passing so far in the postseason.
419 of those yards are on passes to Larry Fitzgerald.

That's better than 12 times the yards of any other Cardinal
receiver except Anquan Boldin (106 yards) and Steve Breaston (77
yards).

The Steelers need to take advantage if and when the Cardinals
turn the ball over. Turnovers were the difference in the
Cardinals' regular season losses to the Redskins, Jets, and
Panthers. The immediate corollary is the Steelers need to
pressure Kurt Warner all game.

The Cardinals have another big weakness: their offense seems to
get really conservative when they have much of a lead. In the
Divisional-round playoff game against the Panthers, it didn't
matter, because Jake Delhomme kept throwing interceptions.
But in the Conference Championship Game, the Cardinals let a
18-point lead slip away. Even in the 4th quarter when they were
driving for the go-ahead score, they seemed to be content to play
for a field goal (which would have given them a very marginal
2-point lead with nearly 3 minutes left for the Eagles to
answer).

With first and goal from the 9, the Cardinals ran on first and
second down, gaining just one yard. On 3rd and goal from the 8,
the Cardinals settled for what appeared to be another give-up
play: a screen pass to running back Tim Hightower. Hightower
actually caught the ball outside the 12 yard line. An Eagle
defender put a solid hit on Hightower at the 2 yard line, and that
should have been the end of the play. But somehow no one wrapped
up on Hightower, and he was able to spin away and into the end zone.
It was almost an afterthought that the Eagles then also
gave up a two-point conversion, which meant a 7-point touchdown
would force overtime, instead of clinching a win.

Wednesday, January 21, 2009

The playoff seeding system was started in 1975. Since then, every
Super Bowl has featured at least one #1- or #2-seeded team.

In the following table, #1 and #2 seeded teams are bolded. Years
marked with a '*' are ones with no #1 seeded team. As usual, the
year refers to when the regular season started; the actual Super
Bowls are played the following calendar year.

Year

Winner

Loser

1975

Steelers #1

Cowboys #4

1976

Raiders #1

Vikings #1

1977

Cowboys #1

Broncos #1

1978

Steelers #1

Cowboys #2

1979

Steelers #2

Rams #3

*

1980

Raiders #4

Eagles #2

*

1981

49ers #1

Bengals #1

1982

Redskins #1

Dolphins #2

1983

Raiders #1

Redskins #1

1984

49ers #1

Dolphins #1

1985

Bears #1

Patriots #5

1986

Giants #1

Broncos #2

1987

Redskins #3

Broncos #1

1988

49ers #2

Bengals #1

1989

49ers #1

Broncos #1

1990

Giants #2

Bills #1

1991

Redskins #1

Bills #1

1992

Cowboys #2

Bills #4

*

1993

Cowboys #1

Bills #1

1994

49ers #1

Chargers #2

1995

Cowboys #1

Steelers #2

1996

Packers #1

Patriots #2

1997

Broncos #4

Packers #2

*

1998

Broncos #1

Falcons #2

1999

Rams #1

Titans #4

2000

Ravens #4

Giants #1

2001

Patriots #2

Rams #1

2002

Buccaneers #2

Raiders #1

2003

Patriots #1

Panthers #3

2004

Patriots #2

Eagles #1

2005

Steelers #6

Seahawks #1

2006

Colts #3

Bears #1

2007

Giants #5

Patriots #1

2008

Steelers #2

Cardinals #4

*

Comments:

There's certainly evidence in this list that high playoff seeds
aren't as valuable as they used to be:

There were 8 #1-vs-#1 matchups 1975 to 1993 (19 seasons).

There were 0 #1-vs-#1 matchups 1994 to 2008 (15 seasons).

Counting this year, we are on a stretch of 5 Super Bowls not
won by a #1 seed. The longest such strech before 2000 was just
two years (1979-1980, and 1987-1988).

The Steelers regain the top spot (they lost the #1 spot
in week
16 after losing to the Titans).

The Cardinals climb to the #9 spot (the highest they've been
since week
9, just before their close win over the 49ers), and 15 spots
higher than they were after their week 16 loss to the Patriots.

There can't be much question that the Cardinals were holding
back the second half of the season. But... why not? After they
lost to the Giants, a bye was pretty well out of reach. One thing
they could do is perpetuate the "same old Cardinals"
stereotype. I think every single team they played underestimated
them. And even now, Mike Tomlin and the Steelers have to be
thinking "just how good are these guys, anyway?" Which
is just about how the Cardinals want it, I would imagine.

In the first half, the Cardinals just dominated. On offense, they
scored at will. On defense, they limited the Eagles to three field
goal tries. The second half was a different story. The Cardinals
play calling seemed to go conservative on both sides of the ball,
while the Eagles started to play with urgency, scoring 3 touchdowns
in 3 drives. But once the Eagles regained the lead, it was their
turn to be conservative: the Cardinals put together a 14 play
touchdown drive that regained the lead, and left the Eagles with
just 62 seconds on the game clock to respond, and they could not.

Ravens (APR, SRS) @ Steelers (Line)

The Ravens demonstrated this season that a good defense can cover
a multitude of offensive shortcomings, including the inexperience of
a rookie quarterback. Holding the Steelers to just 16 points on
offense wasn't quite enough; when Joe Flacco started pressing his
throws, the interceptions started coming, including a game-sealing
pick-6 to Troy Polamalu.

Thursday, January 15, 2009

It's actually happend a fair number of times in the championship
game. In the 40 seasons since 1969, there have been 17 Conference
Championship† Games played by teams in the same division:

†

I'm going to ignore the fact that the 1969 Chiefs @ Raiders
was before the AFL-NFL merger, and so it was the final League
Championship game for the AFL. The playoffs after the 1970 season
featured the first AFC Championship game (not listed).

Year

Division

Game

CC Winner in SB

1969

AFL West

Chiefs @ Raiders

(Chiefs won SB)

1971

AFC East

Colts @ Dolphins

(Dolphins lost SB)

1972

NFC East

Cowboys @ Redskins

(Redskins lost SB)

1977

AFC West

Raiders @ Broncos

(Broncos lost SB)

1978

AFC Central

Oilers @ Steelers

(Steelers won SB)

1979

AFC Central

Oilers @ Steelers

(Steelers won SB)

1980

AFC West

Raiders @ Chargers

(Raiders won SB)

1980

NFC East

Cowboys @ Eagles

(Eagles lost SB)

1982

NFC East

Cowboys @ Redskins

(Redskins won SB)

1982

AFC East

Jets @ Dolphins

(Dolphins lost SB)

1983

AFC West

Seahawks @ Raiders

(Raiders won SB)

1985

AFC East

Patriots @ Dolphins

(Patriots lost SB)

1986

NFC East

Redskins @ Giants

(Giants won SB)

1989

NFC West

Rams @ 49ers

(49ers won SB)

1992

AFC East

Bills @ Dolphins

(Bills lost SB)

1999

AFC Central

Titans @ Jaguars

(Titans lost SB)

2008

AFC North

Ravens @ Steelers

(Steelers won SB)

Comments:

The probability of a same-division matchup seems to be much more
likely in the AFC (12 examples, counting 1969 AFL) than it is in
the NFC (5 examples).

The home team is 11-5 in these games, which is not good news for
the Ravens.

However, the winning team is 9-8 in the Super Bowl,
which suggests this situation is no special advantage to the winning
team once advancing to the Super Bowl.

Wednesday, January 14, 2009

Based on the Divisional rankings. Line values are taken
from yahoo.com,
and are for comparison purposes only.

Picks for week Championship.

Game

APR

SRS

Line

Philadelphia Eagles @Arizona Cardinals

Eaglesρ=1.1375

Eaglesδ=8.85

Eagles-4

Baltimore Ravens @Pittsburgh Steelers

Ravensρ=1.0405

Ravensδ=0.13

Steelers-6

Comments:

The Ravens' biggest problem advancing to the Super Bowl is
going to be how well they recover from the smash-mouth game they
played against the Titans. Even guys that aren't "officially"
injured will still be feeling stiff and sore, moreso as the
Steelers bang them around. The fact that the Steelers'
divisional game was pretty well over early in the 4th quarter
means the Steelers will be fresher for this game.

I didn't think the Cards could beat the Falcons, and surely not
the Panthers, and now I don't think they can beat the Eagles. So
they're a cinch to win, right? Well... the Eagles are coming off
their own smash-mouth game (though less physical than
Ravens/Titans, at least to my eye). Also (as pointed out in
the
Divisional Round Pick Results), the Eagles played a pretty
sloppy game. They will make things a lot harder for themselves if
they give the Cardinals' too many extra chances on Sunday.

The Cardinals are the only remaining team ranked below an
eliminated team. But they are now in the top 12, and finally
above another (albeit eliminated) playoff team.

The Eagles and Steelers are virtually tied. If the Steelers
had held on to their 18-point lead, they would have held on to the
#2 spot.

Since the seeding system was started, Eagles @
Cardinals is just the third championship game without a #1 or
#2 seed. Others were in 1987: Vikings (#5) @ Redskins (#3) and
2006: Patriots (#4) @ Colts (#3).

Certainly the Titans had every chance to win this game, but they
looked out of sync for most of the game. Their offense had 3 long
drives end on a turover. They had at least two bad/early snaps that
could have been (more) disasterous. On the defensive side, the
Ravens were held to just 13 points. But Joe Flacco threw some
passes that should have been knocked down if not intercepted.

Cardinals @ Panthers (APR, SRS, Line)

In week 10, Jake Delhomme threw 4 interceptions to the Raiders,
but the Panthers still managed to pull out the win. This time, they
were playing a team that could actually score given that many extra
chances at the ball. Though it says something about the Cardinals
uncertainty that they kicked so many field goals. A more confident
team would have scored at least 40 points in a game like that.

Eagles @ Giants (APR, SRS, Line)

The Eagles' offense didn't exactly light things up (4 punts, 2
interceptions, and a safety). But the Giants couldn't get into the
end zone, they couldn't convert on critical 3rd and 4th downs. Add
in 2 interceptions and a lost fumble, and it was a very bad day for
Big Blue.

Chargers @ Steelers (APR, SRS, Line)

The Chargers might have had a real chance in this game, except for
a disasterous 3rd quarter. The Steelers' opening drive took 7:56
off the clock and gave them an 11-point lead. The Chargers next two
drives ended on an interception and a muffed punt (and technically,
the muffed punt doesn't count as a possession).

Saturday, January 10, 2009

Since 2001, there have been (at this writing) 98 playoff games
played. Of these, 12 (12.2%) have gone to over time. Here is a
brief summary, for each game, of the team that won the toss, and the
result of their first drive:

It should also be observed that of the 4 games listed above that
were won on the opening overtime drive, the 2009 Saints were the only team that didn't score last in the regulation period. Which suggests to me
that the problem is in the losing teams' defenses, at least as much
as which way the coin-toss went the sample space is too small to draw any useful conclusions.

Comments:

2001 Raiders @ Patriots was the "tuck rule" game. The
Raiders offense never crossed mid-field after the end of the third
quarter. The Patriots scored the final 10 points in regulation,
and drove 61 yards in 15 plays for the game-winning field
goal.

(Since 2001) Most playoff games do not go to overtime.

(Since 2001) Most playoff games that do go to overtime are not
won on the opening drive.

(Since 2001) In the remaining 3 games, there is at least some
evidence that poor defense was as much at fault as the mis-called
toss for losing the game.

Wednesday, January 7, 2009

Based on the Wildcard rankings. Line values are taken
from yahoo.com,
and are for comparison purposes only.

Game

APR

SRS

Line

Arizona Cardinals @Carolina Panthers

Panthersρ=1.1224

Panthersδ=6.60

Panthers-10

Baltimore Ravens @Tennessee Titans

Ravensρ=1.0855

Ravensδ=1.49

Titans-3

San Diego Chargers @Pittsburgh Steelers

Steelersρ=1.0712

Steelersδ=4.56

Steelers-6

Philadelphia Eagles @New York Giants

Giantsρ=1.0042

Giantsδ=0.17

Giants-4

Comments:

Unanimous, except for Ravens @ Titans.

On the one hand, the Ravens have played really strong so far
this season. On the other hand, there seems to be games where
their offense just disappears. They averaged just 10.4
points/game in their five losses.

Tuesday, January 6, 2009

Originally, I was going to measure upset magnatude using the
match-up ratio (the "ρ" value) originally published for the
game. But after some (unposted) analysis, it seems clear that the
match-up ratios are not comparable from week-to-week. They start
out very high at the start of the season, and decline as it goes
on.

So the first modification I made was to use the APR power index
values from the second-to-last week of the season (I avoided the
last week to rule out anomolous effects of teams resting their
starters). However, the normal APR algorithm gives less weight to
early season games.

Rather than try to justify why the week 2 Chargers @
Broncos game was one of the top-10 upsets of the season, I
decided to use the unweighted version of APR power indexes, which
gives all games played equal weight.

Determining the Top 10 Upsets

Using the unweighted APR power indexes for week 17, a list of all
games where the predicted winner lost was compiled. This list was
then sorted according to each game's match-up ratio (ρ).

Any loss that was (in my opinion) attributable to teams not playing
all-out was eliminated from the list. The top 10 games from this
list is presented below.

The Top 10 Upsets of the 2008 Season

As determined by the unweighted APR power indexes from week 16.

Week 5: Buccaneers 13, Broncos 16 (ρ=1.1168)
From week 3 to week 15, APR had the Buccaneers ranked in the top 10.
Maybe they just weren't ready to play at Mile High, but somehow the
Buccaneers let the Broncos give them their second loss.

Week 16: Jets 3, Seahawks 13 (ρ=1.1312)
Because the Jets couldn't put up two touchdowns on the Seahawks, they
went from "win and you're in" to "win (and with help) you're
in". The win and the help never came.

Week 3: Jaguars 23, Colts 21 (ρ=1.1383)
The Jaguars won just 5 games this year, and this was one of them.
It's hard to argue against Peyton Manning as MVP when a key loss like
this is largely attributable to Manning's early season health problems.

Week 7: Jets 13, Raiders 16 (ρ=1.1385)
Because the Jets couldn't put up two touchdowns on the
Raiders... yeah, there seems to be a theme here. You might argue
whether Jets @ Seahawks or Jets @ Raiders is the
bigger upset, but they're both pretty bad.

Week 11: Broncos 24, Falcons 20 (ρ=1.1398)
The Falcons had a chance at the #2 seed going into week 17. If they
had won this game (their only home loss of the season), they would
have had a much better chance.

Week 12: Jets 34, Titans 13 (ρ=1.1398)
At the time, this didn't seem like that much of an upset. But that
was (right) before the Jets went on a 1-4 skid, and finished out of
the playoffs.

Week 17: Raiders 31, Buccaneers 24 (ρ=1.2029)
Coming in to week 17, the Buccaneers still had a chance for the
playoffs (and would've been in, had they won). All they had to do
was beat the 4-11 Raiders. But there was no defense, no win, and no
playoffs.

Week 6: Rams 19, Redskins 17 (ρ=1.2192)
It says something about how bad the Rams were this year that this game
is on this list in spite of the Redskins late-season troubles.

Week 6: Giants 14, Browns 35 (ρ=1.2483)
Easily the low-point to the Giants season. Given the way the offense
was struggling (Eli Manning threw 3 interceptions), the defense would've
needed a masterful performance to keep them in the game. Instead, the
Browns scored at will for much of the game.

Week 7: Cowboys 14, Rams 34 (ρ=1.3023)
Brad Johnson will get his fair share of blame for this loss (the
Cowboys didn't have a second drive for more than 21 yards until
garbage time). But the defense was at fault, too: the Rams scored on
their first 3 drives, and didn't punt for the second time until the
3rd quarter.

If the Cowboys had won this game, they wouldn't have needed a win over
the Eagles in week 17 to get in the playoffs.

Eliminated Games

The only game eliminated from the above list is the Titan's week 15
loss to the Texans (which would have been the #5 upset). At that
point in the season, the Titans had already clinched the AFC South
and a bye week, and only needed to beat the Steelers in week 16 to
clinch the #1 seed in the playoffs. This was a meaningless game for
the Titans.

The Ravens solidify their ranking at #1 with a solid win over
the Dolphins. They will have a tougher challenge next week at the
Titans, though.

The Giants benefit from the Eagles' win and the Colts' loss to
move up to #3.

Peyton Manning now
has 6
one-and-done playoff appearances. I don't know if that's a
record, but after a quick survey, the only others I saw anywhere
close were Joe Montana and Warren Moon, both with 4. (To be
fair, most quarterbacks don't have 6 playoff appearances of any
kind.)

The Cardinals are still way down there. But they did
play the Panthers close in week 8 (losing by 4), so it's not
impossible that the Cardinals could make it to the Championship
game. Which is not a sentence I ever expected to seriously
compose, but there you go.

You can also get an idea of how indirect power affects
rankings, by looking at how, for example, the Bengals and Raiders
swapped places.

I thought I was going to be writing about 4 correctly picked
games. Hah!

Falcons @ Cardinals: wrong

The Cardinals' defense played their best game of the year. They
came up with 2 interceptions, a fumble recovered for a touchdown,
and a safety. The Cardinals' offense had a pretty ordinary day, but
with the defense playing lights-out, it was enough.

Colts @ Chargers: wrong

In their last 4 meetings, the Colts are now 1-3 vs the Chargers
including two playoff games. Scifres (the punter) is clearly the
MVP of the game: the Colts had 10 drives start at or inside their 20
yard line, including 4 at or inside the 10. Sproles running game
was big too, but all those long fields Manning faced was key to the
Chargers holding the Colts to just 17 points.

In the regular season, the Eagles struggled when they couldn't run
the ball, which seems like a problem for them going up against
Minnesota's run defense. And if the Vikings had been able to hold
them to a handful of field goals, it would have been. But Tarvaris
Jackson threw a pick-6, and Brian Wesbrook got free for a long
touchdown reception, and the Vikings just couldn't catch up.